While the early-time observation from Planck provides \(H_0=67.4 \pm 0.5\)  \(\rm km\;s^{-1}Mpc^{-1}\) 
with the \(\Lambda \) CDM scenario [1]}, late-time measurements of \(H_0\)  exceed early-time estimation to the extent more than \(4 \sigma \)  [2]}. This Hubble constant tension may call for new physics beyond \(\Lambda \) CDM with different behavior in early and late times of the universe [3]}, [4]}.
On the other hand, the generalized Proca theory, which has phantom-like behavior of \(w_{DE}\)  with \(s>0\) , naturally favors a larger \(H_0\)  and is helpful to resolve the \(H_0\)  tension [5]}, [6]}, [7]}.
